Tabulae Motuum Quinque Satellitum Saturni ad Fidem Nuperarum Observationum Correctae, Coeloque Conformes Redditae

I. Tabulae Motuum quinque Satellitum Saturni ad fidem nuperarum Observationum correctae, Caloque conformes reddita. Circa finem Anni 1686. D. Jo. Dom. Cassini, Reg. Soc. Sodalis, & in Astronomicis nemini secundus, cum Societate nostrâ inventa sua de motibus quinque Satellitum Saturni communicavit, Epochasque singulorum ad annum ineuntem 1686. eorumque motus diurnos in Epistola N° 187. harum Transact. editâ exhibuit: E quibus datis motuum Tabulas concinnavimus, dictæque Epistolæ subjunctas una edidimus. Cum vero deinde per triginta fere annos nullas omnino Observationes eorum tradiderint, qui soli poterant, Astronomi Galli; cumque aliunde, ob intervallum temporis nimis breve, non nisi laxè periodos Satellitum, praesertim interiorum, definire potuerit praclarissimus Inventor; non prius dictarum Tabularum defectus corrigere datum est, quam in nuperis Actis Academiae Regiae Parisiensis Physicis & Mathematicis, observata ea, quæ sub finem praecedentis Transact. N° 355. protulimus, prodierunt. Horum vero ope facta aliquali Motuum castigatione, tum demum Telescopio Hugeniano omne Saturni Satellitium ipsi agnovimus; adhibitisque accuratis Rev. D. Jac. Pounds observationibus, Tabulas subsequentes caelo satis consonas obtinuimus. Addendo sc. motui annuo Interioris, 2 gr. 9'; Penintimi vero 3°. 25' retentis Epochis D. Cassini ad Annum 1686. Augendo etiam motum annuum Extimi 9 min. sublatis vero 16 grad. ab Epochæ, quæ in Epistola dicta N° 187. perperam scribitur X. 16°. 19', pro X. 0°. 16'. Hugenianum 6' annuatim tardiorum invenimus. Tertii autem Tabellas, ob motum diurnum falsò in Epistola illa traditum, de integro recedere necesse habuimus, retenta saltem Epochæ. Tabula Mediorum Motuum Intimi Satellitis Saturni à Cassino detecti Anno 1686. | Annis Christi inuent | Epochæ | Annis | Mot. Med. | Diebus | Mot. Med. | Mot. Med. Sex. | Motus Med. | |----------------------|--------|-------|-----------|--------|----------|---------------|------------| | | s° | s° | s° | s° | s° | s° | s° | | 1681 | ≈ | 8 48 | 1 4 443 | 1 6 10 42 | 1 0 7 57 | 3 4 6 | | 1686 | ρ | 13 4 | 2 8 9 25 | 2 0 21 24 | 2 0 15 52 | 3 2 4 14 | | 1701 | ρ | 6 34 | 3 0 14 8 | 3 7 2 6 | 3 0 23 50 | 3 3 4 22 | | 1714 | ρ | 9 57 | 4 10 29 33| 4 1 12 47| 4 0 31 47| 3 4 4 30 | | 1715 | ≈ | 14 39 | 5 3 4 16 | 5 7 2 29| 5 0 39 44| 3 5 4 38 | | 1716 | II | 19 22 | 6 7 8 59 | 6 2 4 11| 6 0 47 40| 3 6 4 46 | | 1717 | ρ | 4 47 | 7 11 13 42| 7 8 14 53| 7 0 55 37| 3 7 4 54 | | 1718 | ρ | 9 30 | 8 9 29 6 | 8 2 25 35| 8 1 3 43 38| 3 8 5 2 | | 1719 | ρ | 14 12 | 9 2 3 49 | 9 9 6 17| 9 1 11 31| 3 9 5 10 | | 1720 | ρ | 18 55 | 10 6 8 32 | 10 3 16 59| 10 1 19 28| 4 0 5 18 | Men/Anni Com. | Mot. Med. | s° | |-----------|----| | 11 10 13 15 | 11 | | 12 8 28 40 | 12 | | 13 1 3 23 | 13 | | 14 5 8 5 | 14 | | 15 9 12 48 | 15 | Jan. Febr. | s° | |----| | 3 1 10 | | 8 2 48 | | 6 2 3 44 | | 11 2 5 22 | | 10 1 6 19 | Mar. April Maii | s° | |----| | 16 7 28 13 | | 17 0 2 56 | | 18 4 7 39 | | 19 8 12 21 | | 20 6 27 46 | Juni Julii Aug. Sept. | s° | |----| | 21 1 14 39 | | 22 7 25 21 | | 23 2 6 3 23 | | 24 8 16 45 | | 25 2 27 27 | Octob Nov. Dec. | s° | |----| | 26 9 8 9 26 | | 27 3 18 5 0 | | 28 9 29 3 28 | | 29 4 10 14 | | 30 10 20 5 6 | In Anno Bissextili post Februarium adde unius diei motum. Tabula Mediorum Motuum Satellitis Saturni Penintimi, à Cassino detecti Anno 1686. | Annis | Epocha | Anni | Med. Mot. | Diebus | Med. Mot. | Mot. Mot. | Motus Med. | |-------|--------|------|-----------|--------|-----------|-----------|------------| | Jul. | s o | s o | s o | s o | s o | s o | s o | | 1681 | X | 3 | 23 | 1 | 4 | 10 | 2 | | 1686 | X | 5 | 25 | 2 | 8 | 20 | 4 | | 1701 | X | 22 | 3 | 3 | 1 | 0 | 6 | | 1714 | Vp | 7 | 5 | 4 | 9 | 21 | 40 | | 1715 | X | 17 | 7 | 5 | 2 | 1 | 42 | | 1716 | m3 | 27 | 9 | 6 | 6 | 11 | 44 | | 1717 | II | 18 | 43 | 7 | 10 | 21 | 46 | | 1718 | m3 | 28 | 45 | 8 | 7 | 13 | 20 | | 1719 | X | 8 | 47 | 9 | 11 | 23 | 22 | | 1720 | S | 18 | 49 | 10 | 4 | 3 | 24 | Mens. An. Co. | Jan. | 0 | 0 | 0 | 14 | 1 | 25 | 4 | | Febr. | 3 | 27 | 34 | 15 | 6 | 5 | 6 | | Mar. | 6 | 20 | 32 | 16 | 2 | 26 | 4c | | Apr. | 10 | 18 | 6 | 17 | 7 | 6 | 42 | | Maii | 10 | 4 | 7 | 18 | 11 | 16 | 44 | | Junii | 2 | 1 | 41 | 19 | 3 | 26 | 46 | | Juli | 1 | 17 | 43 | 20 | 0 | 18 | 2c | Aug. | 5 | 15 | 17 | 40 | 1 | 6 | 4c | | Sept. | 9 | 12 | 51 | 60 | 1 | 25 | 0 | | Oct. | 8 | 28 | 53 | 80 | 2 | 13 | 20 | | Nov. | 0 | 26 | 27 | 100 | 3 | 1 | 4 | | Dec. | 0 | 12 | 28 | 120 | 3 | 20 | 0 | In Anno Bissextili post Februarium adde unius diei motum. Tabula Mediorum Motuum Satellitis Saturni Medii, à Cassino detecti Anno 1671. | Annis Juliae ineunt | Epochæ | Med. Motus | Med. Motus | Med. Motus | Med. Motus | |---------------------|--------|------------|------------|------------|------------| | | s o | s o | s o | s o | s o | | 1681 | 12 | 16 | 9 | 17 | 2 | | 1686 | 27 | 6 | 7 | 4 | 3 | | 1701 | 1 | 17 | 4 | 21 | 5 | | 1714 | 11 | 43 | 4 | 27 | 48 | | 1715 | 28 | 45 | 2 | 14 | 50 | | 1716 | 15 | 47 | 6 | 1 | 52 | | 1717 | 22 | 30 | 9 | 18 | 53 | | 1718 | 9 | 32 | 9 | 25 | 36 | | 1719 | 26 | 34 | 9 | 7 | 38 | | 1720 | 13 | 35 | 10 | 4 | 29 | | Mens. Anni Com. | | | | | | | Jan. | | | | | | | Febr. | | | | | | | Mar. | | | | | | | Apr. | | | | | | | Mai | | | | | | | Jun. | | | | | | | Julii | | | | | | | Aug. | | | | | | | Sept. | | | | | | | Oct. | | | | | | | Nov. | | | | | | | Dec. | | | | | | In Anno Bissextili post Februarium adde unius Diei motum Tabula Mediorum Motuum Penextimi Sattelitis Saturni ab Hugenio inventi Anno 1655. | Annis Ful. | Epochs | Annis | Med. Mot. | Diebus | Med. Mot. | Sid. Mot. | Motus | |------------|--------|-------|-----------|--------|-----------|----------|-------| | incunt | s o i | s o i | s o i | s o i | s o i | s o i | s o i | | 1641 | 2 48 | 1 10 | 20 35 | 1 0 22 | 35 | 0 66 | 31 29 10 | | 1661 | 13 23 | 2 9 | 11 10 | 2 1 | 15 9 | 2 53 | 23 30 6 | | 1681 | 27 58 | 3 8 | 1 45 | 3 2 | 7 44 | 3 49 | 33 31 3 | | 1686 | m 3 28 | 4 7 | 14 55 | 4 3 | 0 18 | 3 46 | 34 31 59 | | 1701 | II 12 | 3 6 | 5 30 | 5 3 | 22 53 | 5 44 | 32 55 | | 1714 | X 17 | 5 6 | 4 26 | 5 6 | 4 15 28 | 6 59 | 33 52 | | 1715 | 8 28 | 7 3 | 16 40 | 7 5 | 8 2 | 7 65 | 37 48 | | 1716 | 29 3 | 8 2 | 29 50 | 8 6 | 0 37 | 8 71 | 38 45 | | 1717 | 12 13 | 9 1 | 20 25 | 9 6 | 23 12 | 9 82 | 39 41 | | 1718 | m 2 48 | 10 0 | 11 0 | 10 7 | 15 46 | 10 94 | 40 38 | | 1719 | 23 23 | 11 11 | 1 35 | 11 8 | 8 21 | 11 10 | 21 41 38 34 | | 1720 | 13 58 | 12 10 | 14 45 | 12 9 | 0 55 | 12 11 | 17 42 39 31 | | 1721 | 27 8 | 13 9 | 5 20 | 13 9 | 23 30 | 13 12 | 14 43 40 27 | | Mens. Anno | Med. Mot. | s o i | s o i | s o i | s o i | s o i | s o i | | Jan. | 0 0 0 | 16 5 | 29 40 | 16 0 | 1 14 | 16 15 | 3 46 43 17 | | Febr. | 9 54 | 17 4 | 20 15 | 17 0 | 23 48 | 17 16 | 0 47 44 13 | | Mar. | 8 12 | 18 3 | 10 50 | 18 1 | 16 23 | 18 16 | 5 48 45 10 | | Apr. | 7 21 | 19 2 | 1 25 | 19 2 | 8 58 | 19 17 | 5 249 46 6 | | Maii | 6 9 | 14 20| 1 14 35 | 20 3 | 1 32 | 20 18 | 49 50 47 3 | | Junii | 5 19 | 40 2 | 29 10 | 21 3 | 24 7 | 21 19 | 45 51 47 59 | | Julii | 4 6 | 26 60| 4 13 45 | 22 4 | 16 42 | 22 20 | 42 52 48 56 | | Aug. | 3 16 | 18 80| 5 28 20 | 23 5 | 9 16 | 23 21 | 38 53 49 52 | | Sept. | 2 26 | 12 100| 7 12 55 | 24 6 | 1 51 | 24 22 | 35 54 50 49 | | Oct. | 1 13 | 30 120| 8 27 3 | 25 6 | 24 25 | 25 23 | 31 55 51 45 | | Nov. | 0 23 | 24 140| 10 12 5 | 26 7 | 17 0 | 26 24 | 27 56 52 42 | | Dec. | 11 10 | 42 160| 11 26 40 | 27 8 | 9 35 | 27 25 | 24 57 53 38 | | In Anno Bissextili post Februarium adde unius diei motum. | | | | | | | | In Anno Bissextili post Februarium adde unius diei motum. Tabula Mediorum Motuum Satellitis Saturni Extimi, à Cassino detecti Anno 1671. | Annis | Epochen | Anni | Med. Motus | Diebus | Med. Motus | Mo. Me. | Med. Motus | |-------|---------|------|------------|--------|------------|--------|------------| | Julii | ineunt | s o | s o | s o | s o | s o | s o | | 1681 | V 8 40 | 1 7 6 32 | 1 0 4 32 | 1 0 11 31 | 5 51 | | 1686 | V 15 50 | 2 2 13 3 | 2 0 9 5 | 2 0 23 32 | 6 3 | | 1701 | V 11 53 | 3 9 19 35 | 3 0 13 37 | 3 0 34 33 | 6 14 | | 1714 | X 20 20 | 4 5 0 39 | 4 0 18 9 | 4 0 45 34 | 6 25 | | 1715 | X 26 52 | 5 0 7 10 | 5 0 22 42 | 5 0 57 35 | 6 37 | | 1716 | II 3 23 | 6 7 13 42 | 6 0 27 14 | 6 1 8 36 | 6 48 | | 1717 | W 14 27 | 7 2 20 13 | 7 1 1 46 | 7 1 19 37 | 7 0 | | 1718 | O 20 58 | 8 10 1 17 | 8 1 6 18 | 8 1 31 38 | 7 11 | | 1719 | X 27 30 | 9 5 7 49 | 9 1 10 51 | 9 1 42 39 | 7 22 | | 1720 | m 4 2 | 10 0 14 20 | 10 1 15 23 | 10 1 53 40 | 7 34 | Mens. Med. Motus | Anni Com. | Jan. | Febr. | Mar. | Apr. | Maii | Jun. | Julii | Aug. | Sept. | Oct. | Nov. | Dec. | |-----------------|----------|------|------|------|------|------|------|-------|------|-------|------|------|------| | 11 7 20 52 | 12 3 1 56 | 14 5 14 59 | 15 0 21 30 | 16 8 2 34 | 17 3 9 6 | 18 10 15 37 | 19 5 22 9 | 20 1 3 13 | 21 3 5 18 | 22 3 9 5 | 23 3 14 23 | 24 3 18 55 | 25 3 23 28 | | 11 1 19 55 | 12 1 24 28 | 14 2 3 32 | 15 2 8 5 | 16 2 12 37 | 17 2 17 9 | 18 2 21 42 | 19 2 26 14 | 20 3 0 46 | 21 3 5 18 | 22 3 9 5 | 23 3 14 23 | 24 3 18 55 | 25 3 23 28 | | 11 2 5 41 | 12 2 16 42 | 14 2 3 32 | 15 2 8 5 | 16 2 12 37 | 17 2 17 9 | 18 2 21 42 | 19 2 26 14 | 20 3 0 46 | 21 3 5 18 | 22 3 9 5 | 23 3 14 23 | 24 3 18 55 | 25 3 23 28 | In Anno Bisextili post Februarium adde unius Diei motum. Motibus mediis Satellitum ad hunc modum constitu- tis, proveniunt Revolutiones eorum jam veris proximæ, scilicet | Primi sive Intimi | Secundi Penintimi | Tertii sive Medii | Quarti Hugeniani | Quinti sive Extimi | |-------------------|-------------------|------------------|-----------------|-------------------| | 1. 2°. 18. 26½ | 2. 17. 41. 10½ | 4. 12. 25. 10 | 15. 22. 41. 28 | 79. 7. 46. 00 | Posito autem, juxta regulam Naturæ (saltem in hoc nostro Systemate) universalem quæque tam in Jovialium ac Lunæ motibus, quam Planetarum Primariorum circa Solem, obtinet, Vires centrum Saturni petentes esse in duplicata ratione distantiarum reciproce, ac proinde Cubos distantiarum à centro esse ut quadrata Temporum periodicorum; ex data distantia & periodo Hugeniani, fiunt reliquorum distantiæ ut sequitur. | Dist. Primi | Secundi | Tertii | Quartii | Quinti | |-------------|---------|--------|---------|--------| | 1.9289 | 2.4708 | 3.4508 | 8.0000 | 23.3146| Quæ quidem distantiæ cum D. Cassini observatis satis qua- drant. Quatuor autem interiores Satellites juxta planum Annuli Saturni orbitas suas describunt proximè; in pla- no. sc. Æquatoris nostri plano quoad sensum parallelo, quicquid in contrarium proferant nonnulli. Quintum ve- ro orbem situ paulo diversum à cæteris describere, nuper prehendit D. Jac. Cassinus prioris filius & virtutum hæres, ut videre est in Actis Academiæ Scientiarum Parisiensis Anni 1714. Sed hæc autem omnia propriis oculis con- templari, atque penitus introspicere jam ipsi accingimur.